## Algebra 2 (1st Edition)

$63$
From part (a): $a_n= a_1 r^{n-1}$ ...(1) Here, we have Common Ratio $r=\dfrac{1}{2}$ and first term $a_1=32$ Equation (1) gives: $a_n=32 \times (\dfrac{1}{2})^{n-1}$ This implies that $n = 6$ We know that $S_{n}=a_1(\dfrac{1-r^{n}}{1-r})$ Now, $S_{6}=32 \times (\dfrac{1-(1/2)^{n}}{1-\dfrac{1}{2}})$ $S_{6}=32 \times (\dfrac{1-(1/2)^{n}}{-\dfrac{1}{2}})$ Hence, $S_{6}=63$